Help with a study guide question, i will give best response. (Attached file.) Please Help me! I'm study for a big test

- Ms-Brains

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- Ms-Brains

##### 1 Attachment

- freckles

apply distributive property where possible
distributive property says a(b+c) is equal to ab+ac
I see you have 3(x-y)
apply distributive property there

- freckles

you can tell me what you get when you apply distributive property to 3(x-y)?

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## More answers

- Ms-Brains

3xy? or 3(y-x) p
Idk how to do the distributive property

- freckles

you do see distributive property is a(b+c)=ab+ac
we are taking the outer number and multiplying it to both terms inside the ( )?

- freckles

example
6(2+7) is the same as 6*2+6*7
though we didn't need distributive property here because we know what 2+7 is...
6(2+7)=6(9)=54
but we see we get the same number using the distributive property
6(2+7)=6*2+6*7=12+42=54

- freckles

here we can't do y take away x because we don't know what x and y are
so you have to apply distributive property here where you have 3(x-y)

- freckles

3(x-y) is the same as 3x-3y

- freckles

\[3x+4y+3(x-y)-4x \\ 3x+4y+3x-3y-4x\]

- freckles

now using that addition is commutative to place like terms together

- freckles

commutative property is just changing the order

- Ms-Brains

so for the first slot it's written like 3x+4y+3x-3y-4y = Distributive property??

- freckles

almost

- freckles

you want to leave that last term as it was
we didn't do anything to it

- Ms-Brains

Umm, how do you write exactly?
I'm a little lost on what your saying...sorry

- freckles

should be 3x+4y+3x-3y-4x by use of the distributive property

- freckles

-4x doesn't just turn into -4y

- Ms-Brains

Oh! I got it! Okay give me a sec to write it, and then we can move to the next slot?

- Ms-Brains

I got it! so next one?

- freckles

have you tried changing the order to put like terms together yet? that was what I suggested above.... I also gave the name of this property too. :)
You try it and I will check it.

- Ms-Brains

Wait, what do you want me to do?

- freckles

change the order so like terms are together

- freckles

like terms are terms with the same variable part

- freckles

you should see three terms that have the common variable x
you should see two terms that have the common variable y

- freckles

put all your x terms together and put all your y terms together

- Ms-Brains

10x +7y
Like that?

- Ms-Brains

@freckles

- freckles

like if I had a+a+b+a+b-4a
reorder so that like terms are together
a+a+a-4a+b+b

- Ms-Brains

3x+3x+4x=10x
4y+3y=7

- Ms-Brains

^^ That?

- freckles

you shouldn't change the sign in front of the term
you had
3x+4y+3x-3y-4x
by commuative property we can write this as
3x+3x-4x+4y-3y

- Ms-Brains

Oh... I was supposed to add all the X's in order, and all the y's after that?

- freckles

Example:
\[a+a+b+a+4(\frac{1}{4}b-a) \text{ given } \\ a+a+b+a+4 \cdot \frac{1}{4} b-4a \text{ by distributive property } \\ a+a+b+a+b-4a \text{ by simplification } \\ a+a+a-4a+b+b \text{ by commutative property } \\ (a+a+a-4a)+(b+b) \text{ by associative property } \\ a(1+1+1-4)+b(1+1) \text{ by distributive property } \\ a(-1)+b(2) \text{ by simplification } \\ -a+2b \text{ by commautive property }\]

- freckles

anyways I be back
I have thing

- Ms-Brains

Wait you're leaving?! I thought you'd help me finish the problem??

- Ms-Brains

@freckles COME BACK!!!!!

- Ms-Brains

Math tease.

- freckles

Sorry. I had something come up.
Anyways I hoped the example helped.

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